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There is now strong evidence that some stars have been born with He mass fractions as high as Y≈0.40 (e.g. in ω Centauri). However, the advanced evolution, chemical yields, and final fates of He-rich stars are largely unexplored. We investigate the consequences of He-enhancement on the evolution and nucleosynthesis of intermediate-mass asymptotic giant branch (AGB) models of 3, 4, 5, and 6 M⊙ with a metallicity of Z = 0.0006 ([Fe/H] ≈-1.4). We compare models with He-enhanced compositions (Y =...[Show more] 0.30, 0.35, 0.40) to those with primordial-He (Y = 0.24). We find that the minimum initial mass for C burning and super-AGB stars with CO(Ne) or ONe cores decreases from above our highest mass of 6 to ~4-5M⊙ with Y = 0.40. We also model the production of trans-Fe elements via the slow neutron-capture process (sprocess). He-enhancement substantially reduces the third dredge-up efficiency and the stellar yields of s-process elements (e.g. 90 per cent less Ba for 6 M⊙, Y = 0.40). An exception occurs for 3 M⊙, where the near-doubling in the number of thermal pulses with Y = 0.40 leads to ~50 per cent higher yields of Ba-peak elements and Pb if the 13C neutron source is included. However, the thinner intershell and increased temperatures at the base of the convective envelope with Y = 0.40 probably inhibit the 13C neutron source at this mass. Future chemical evolution models with our yields might explain the evolution of s-process elements among He-rich stars in ω Centauri.